CN114462124A - Establishment and numerical simulation method of a three-dimensional multiphase mesoscopic model of concrete - Google Patents

Abstract

The invention relates to a method for establishing and numerically simulating a three-dimensional multiphase mesoscopic model of concrete. First, a three-dimensional random aggregate model of concrete is established, an interface transition zone layer is expanded in the geometric model, and an internal and external grid transition surface is set to effectively reduce the number of units; On this basis, considering the inconsistency of the interface transition zone, a three-dimensional multiphase mesoscopic model of concrete is established; the tensile-plastic damage constitutive relationship of the concrete specimen material is defined; the numerical value of the three-dimensional failure failure process of the concrete specimen is carried out by using the displacement loading method. Simulation, the damage and fracture situation inside the concrete is simulated and analyzed, and the model established based on this application can more clearly show the damage evolution process of the concrete as a three-dimensional space structure.

Description

Establishment and numerical simulation method of a three-dimensional multiphase mesoscopic model of concrete

technical field

The invention relates to a method for establishing and numerically simulating a three-dimensional multiphase mesoscopic model of concrete, and belongs to the field of numerical simulation of concrete materials.

Background technique

In recent years, my country's urbanization process has been advancing continuously, and major infrastructure construction and engineering construction are in the stage of rapid development. Large-scale projects such as concrete dams, concrete protective shells of nuclear power plants, towering buildings, high-speed railways, and cross-sea bridges are closely related to concrete materials. There is a close relationship, and the construction of modern projects also puts forward higher requirements for the performance of concrete materials. As one of the most widely used building materials, the safety and reliability of concrete directly affect the safety of building structures.

The heterogeneity of concrete itself and its complex internal structure make its failure mechanism very complicated. According to different research focuses, scholars have established various concrete mesoscopic models. The multiphase mesoscopic model takes into account the heterogeneity of concrete and the different mechanical parameters of each phase, so it has advantages in the simulation of concrete failure and failure.

Due to the relatively simple modeling and calculation process of the two-dimensional concrete meso-model, the early researches mostly focused on the two-dimensional level, but in practical engineering, it can be simplified to plane stress problems (such as thin plates) and plane strain problems (such as gravity dams) In addition to the three-dimensional problems of concrete, many problems are difficult to be simplified into two-dimensional problems for analysis. It is of great significance and value to study the failure and failure process of concrete by using three-dimensional mesoscopic models.

In the meso-scale, the interface transition zone is an important part of concrete that cannot be ignored. In the three-dimensional model, for the consideration of the amount of calculation, the interface transition zone is generally simplified to different degrees, and the fine mesh is used for it. less. Due to the limitation of computer capability in 3D mesoscopic analysis, there are inevitably problems such as excessive simplification steps and unreasonable analysis process, resulting in unsatisfactory analysis results of 3D models. In order to facilitate the establishment of the model, many 3D models simplify the aggregate shape to spherical, but this is an ideal simplification; some 3D mesoscopic studies only regard concrete as a two-phase material, while ignoring the interface transition zone. Most studies do not consider the non-uniformity of the interface transition zone, and treat the interface transition zone outside of different aggregates as materials with the same material properties, which inevitably affects the calculation results. The interface transition zone is the weak link of concrete materials, and it is essential to consider the interface transition zone in the mesoscopic analysis. Therefore, the optimization of the interface transition zone model in the 3D mesoscopic model is also one of the important aspects of current research.

SUMMARY OF THE INVENTION

The invention provides a method for establishing and numerically simulating a three-dimensional multiphase mesoscopic model of concrete, and introduces a method for establishing and numerically simulating a three-dimensional multiphase mesoscopic model of concrete. inconsistency.

The technical scheme adopted by the present invention to solve its technical problems is:

A method for establishing and numerically simulating a three-dimensional multiphase mesoscopic model of concrete, specifically comprising the following steps:

Step S1: establishing a concrete three-dimensional random aggregate model, and the concrete three-dimensional random aggregate model includes a three-dimensional spherical aggregate model, a three-dimensional ellipsoid aggregate model, and a three-dimensional random convex polyhedron aggregate model;

Step S2: Based on the concrete three-dimensional random aggregate model established in step S1, define the aggregate unit, and at the same time define the mortar unit according to the size of the concrete specimen, and establish a three-dimensional multiphase mesoscopic model of the non-uniform concrete in the interface transition zone;

Step S3: setting the inner and outer mesh transition surfaces for the non-uniform concrete three-dimensional multiphase mesoscopic model of the interface transition zone;

Step S4: Based on the model obtained in Step S3, use the displacement loading method to perform numerical simulation of the three-dimensional failure failure process of the concrete specimen;

As a further preference of the present invention, in step S1, the steps of establishing a three-dimensional random aggregate model of concrete are as follows:

Step S11: Determine the number of aggregates in each particle size range, and use the Fuller gradation formula to obtain the percentage of aggregate in each particle size range to the total aggregate volume. The Fuller gradation formula is:

In formula (1), D ₀ is the diameter of the sieve hole, D _max is the maximum particle size of the aggregate passing through the sieve hole, P _c (D<D ₀ ) is the cumulative volume percentage of aggregate passing through the sieve hole with a diameter of D ₀ , That is, the percentage of aggregate in the particle size range to the total volume;

Substitute the percentage of aggregates in the obtained particle size range into the total volume into formula (2) to determine the number of aggregates in each particle size range, formula (2) is:

In formula (2), D _i is the representative particle size of the aggregate in this particle size range, V is the total aggregate volume, and P _ci is the percentage of aggregate volume in this particle size range to the total aggregate volume;

Step S12: according to the Monte Carlo principle, randomly generate the parameters of the aggregates in each particle size range, and the parameters include the position and size parameters of the aggregates;

Step S13: using the obtained aggregate parameters within each particle size range to judge the separation of aggregates, that is, to judge the separation of spherical aggregates, ellipsoid aggregates and random convex polyhedron aggregates;

Step S14: Embed the Python program of the aforementioned judgment result into ABAQUS to generate a three-dimensional random aggregate geometric model;

As a further preference of the present invention, in step S13, the judgment of the separation of aggregates mainly includes a method for judging the validity of spherical aggregates, a quadratic matrix of space ellipsoids, and a method for judging the validity of ellipsoid aggregates;

Among them, the method for determining the effectiveness of spherical aggregates is: set spherical aggregates A _i (x _ci , y _ci , z _ci ), spherical aggregates A ₀ (x _c0 , y _c0 , z _c0 ), spherical aggregates A _i , the radii of spherical aggregate A ₀ are _ri and r ₀ respectively, then the judgment equation is

Then, let the coordinates of the lower left corner and upper right corner of the bounding cuboid be (x _L , y _L , z _L ) and (x _U , y _U , z _U ) respectively, the center of each spherical aggregate is A _i , and the spherical The center coordinates are (x _ci , y _ci , z _ci ) and the radius is r _i , then the judgment equation for the separation of spherical aggregate A _i from the boundary is:

The spherical aggregate A ₀ is a random convex polyhedron aggregate generated by the inscribed method on the basis of the spherical aggregate A _i . The positions of the vertices of the random convex polyhedral aggregate A ₀ are random and the spherical surface of the spherical aggregate A _i is circumscribed. , the coordinates of each vertex of the random convex polyhedron are expressed as

In formula (4), the spherical center coordinates of spherical aggregate A ₀ are (x _c0 , y _c0 , z _c0 ), the radius is r ₀ , the coordinates are set to start from the y-axis, and the clockwise direction is positive, α _i is the offset angle from the z-axis, and the clockwise direction is positive, and β _i is the angle rotated around the center of the sphere in the xOy plane;

Then, similarly, let the coordinates of the lower left corner and upper right corner of the bounding cuboid be (x _L , y _L , z _L ) and (x _U , y _U , z _U ) respectively, then the random convex polyhedron aggregate A ₀ and The judgment equation for boundary separation is:

The method for judging the validity of ellipsoid aggregates is: set the quadratic forms of ellipsoid A and ellipsoid B as X ^T AX=0 and X ^T BX=0, respectively, then the generalized characteristic polynomials of ellipsoid A and ellipsoid B are for

f(λ)=det(λA+B),

If the equation f(λ)=0 has two different positive real roots, then ellipsoid A and ellipsoid B are separated; otherwise, ellipsoid A and ellipsoid B intersect;

Then, the method for judging the separation of the ellipsoid aggregate from the boundary is: combine the equations of the ellipsoid and the plane to obtain the matrix equation

是一个三阶对称方阵，In formula (6),

is a third-order symmetric square matrix,

若矩阵A和B满足条件|A|>0且(a₁₁+a₂₂)|B|<0，则椭球与平面相交，否则，椭球与平面相离；let matrix

If the matrices A and B satisfy the conditions |A|>0 and (a ₁₁ +a ₂₂ )|B|<0, then the ellipsoid intersects the plane, otherwise, the ellipsoid is separated from the plane;

As a further preference of the present invention, the specific steps of establishing a three-dimensional multiphase mesoscopic model of the non-uniform concrete in the interface transition zone in step S2 are:

Step S21: Define the tensile-plastic damage constitutive relation and determine the material parameters. The tensile-plastic damage constitutive relation formula is:

In formula (7), σ _tu is the peak stress of the material, G _f is the fracture energy, and u ^ck is the cracking displacement;

Step S22 : establishing a three-dimensional multiphase mesoscopic model of the non-uniform concrete in the interface transition zone, including a linear proportional relationship between the thickness of the interface transition zone and the aggregate particle size, and an exponential function relationship between the strength of the interface transition zone and the thickness of the interface transition zone. The relationship between the strength of the transition zone and the thickness of the interface transition zone is

ξ=e ^bδ-c +d (8)

In formula (8), ξ is the ratio of the strength of the interface transition zone to the mortar strength, δ is the thickness of the interface transition zone, c and d are the parameters of the exponential function, the coordinates of two points (δ _min , ξ _max ) and (δ _max , ξ _min ) is substituted into the expression to obtain;

Step S23: Based on formula (8), determine the material parameters of the concrete specimen, substitute the determined mortar strength, interface transition zone strength and fracture energy into formula (7), determine the mortar and interface transition zone plastic damage parameters, use Python script Programmatically generate σ _t -u ^ck and d _t -u ^ck table functions;

Step S24: wrapping the interface transition area with a thickness outside the aggregate, and using the cutting and merging operations of the Assembly module in ABAQUS to complete;

As a further preference of the present invention, in step S3, a high-density mesh is arranged in the interface transition area, the size of the seed is equivalent to its thickness, sparse meshes are arranged in the aggregate unit and the mortar unit, and the interface transition area is respectively connected with the aggregate. A mesh transition surface is set at the junction of the unit and the mortar unit, so that the high-density mesh in the interface transition area can smoothly transition to the sparse mesh of the aggregate unit and the mortar unit;

As a further preference of the present invention, the method for establishing the mesh transition surface is as follows: in the aggregate unit inside the interface transition area and the mortar unit outside the interface transition area, a concentric concentric with the aggregate centroid and different particle size is established respectively. noodle;

As a further preference of the present invention, the specific steps of step S4 are:

Step S41 : applying boundary conditions to the non-uniform concrete three-dimensional multiphase mesoscopic model of the interface transition zone to be tested, and applying displacement loads at the loading points;

Step S42 : setting a damage threshold, when the tensile damage value reaches the damage threshold, it is determined that the unit fails to cause fracture damage. The larger the damage value is, the more serious the material failure and damage is, and the damage threshold is 0.9;

Step S43: storing the acquired damage value in the result information matrix, and processing the elements in the result information matrix after the calculation to complete the simulation of the three-dimensional damage evolution process and fracture shape of the concrete specimen;

As a further preference of the present invention, when the three-dimensional multiphase mesoscopic model of concrete is tested and simulated, after setting the damage threshold, the failure failure mode and the degree of damage and fracture of the material are described with the damage cloud map at the end of the ABAQUS calculation;

At the same time, when the load is applied to the lateral boundary of the uniaxial tensile specimen, the damage evolution process and failure failure mode of multiple sections of the concrete specimen are analyzed.

Through the above technical solutions, with respect to the prior art, the present invention has the following beneficial effects:

1. The present invention establishes a three-dimensional spherical aggregate model, a three-dimensional ellipsoid aggregate model and a three-dimensional random convex polyhedron aggregate model, and uses a more accurate method to determine the separation between aggregate and boundary, and between aggregate and aggregate. It can greatly reduce the time required to judge the separation of aggregates;

2. The present invention considers the inconsistency of the interface transition zone in the three-dimensional multiphase mesoscopic model of concrete, that is, the thickness and strength of the interface transition zone outside each aggregate change with the change of aggregate particle size, which truly reflects the interface. Mechanical properties of the transition zone;

3. In the present invention, mesh transition surfaces are respectively set in the aggregate unit inside the interface transition area and the mortar unit outside the interface transition area, which fully reflects the characteristics of the concrete three-dimensional multiphase mesoscopic model and effectively reduces the total number of units in the model. , which improves the computational efficiency of the model;

4. The present invention adopts multiple micro-sections to analyze the three-dimensional failure and failure process of the concrete specimen, and compares the damage cloud image of the transition area of the inner interface of the concrete specimen with the macro damage cloud image of the outer side of the specimen, so as to clearly show the concrete specimen as the The damage evolution process of a three-dimensional structure.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

Fig. 1a-Fig. 1b are aggregate models provided by the present invention, wherein Fig. 1a is a three-dimensional ellipsoid aggregate model, and Fig. 1b is a three-dimensional random convex polyhedron aggregate model;

Fig. 2 is the relation curve between the strength of the interface transition zone and the thickness of the interface transition zone;

Fig. 3a-Fig. 3b are the interface transition regions of different aggregates, wherein Fig. 3a is the interface transition region of ellipsoid aggregates, and Fig. 3b is the interface transition region of convex polyhedron aggregates;

Figures 4a-4b are schematic diagrams of meshing the interior of different aggregates, wherein Figure 4a is an ellipsoid aggregate, and Figure 4b is a convex polyhedron aggregate;

Figures 5a-5c show the damage evolution process and failure failure modes of different sections during the simulation test of the concrete specimen;

Figures 6a-6b are the overall fracture diagram and fracture morphology diagram of the concrete specimen at the end of model loading, wherein Figure 6a is the overall fracture diagram, and Figure 6b is the fracture morphology.

Detailed ways

The present invention will now be described in further detail with reference to the accompanying drawings. In the description of the present application, it should be understood that the orientation or positional relationship indicated by the terms "left side", "right side", "upper", "lower part", etc. are based on the orientation or positional relationship shown in the drawings, only For the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the referred device or element must have a particular orientation, be constructed and operate in a particular orientation, "first", "second", etc. importance, and therefore should not be construed as a limitation to the present invention. The specific dimensions used in this embodiment are only for illustrating the technical solution, and do not limit the protection scope of the present invention.

As explained in the background art, in the current simulation test on the failure and damage of concrete, the part of the interface transition zone is often ignored, so there is a great hidden danger to the accuracy of the test calculation result.

Therefore, this application provides a method for establishing a three-dimensional multiphase mesoscopic model of concrete and numerical simulation. The inconsistency of the transition zone can clearly show the damage evolution process of the concrete specimen as a three-dimensional structure.

Specifically, it includes the following steps:

Step S1: establish a concrete three-dimensional random aggregate model, and the concrete three-dimensional random aggregate model includes a three-dimensional spherical aggregate model, a three-dimensional ellipsoid aggregate model and a three-dimensional random convex polyhedron aggregate model; each model is established here, using more The accurate method to determine the separation between aggregates and boundaries, between aggregates and aggregates, can greatly reduce the separation of aggregates compared with the previous method in which the distance between the centers of the ellipsoids is greater than the sum of the two major semi-axes. To judge the time required, it is also necessary to explain why only spherical, ellipsoid (Fig. 1a) and convex polyhedral aggregate (Fig. 1b) models are established. Strictly speaking, it includes a variety of aggregate structures, but the general aforementioned The three types of aggregate models can cover most situations and fully meet the needs of experimental simulation;

The specific steps are:

Step S11: Determine the number of aggregates in each particle size range, and use the Fuller gradation formula to obtain the percentage of aggregate in each particle size range to the total aggregate volume. The Fuller gradation formula is:

In formula (1), D ₀ is the diameter of the sieve hole, D _max is the maximum particle size of the aggregate passing through the sieve hole, P _c (D<D ₀ ) is the cumulative volume percentage of aggregate passing through the sieve hole with a diameter of D ₀ , That is, the percentage of aggregate in the particle size range to the total volume;

Substitute the percentage of aggregates in the obtained particle size range into the total volume into formula (2) to determine the number of aggregates in each particle size range, formula (2) is:

In formula (2), D _i is the representative particle size of the aggregate in this particle size range, V is the total aggregate volume, and P _ci is the percentage of aggregate volume in this particle size range to the total aggregate volume; during the test, P _ci That is, the percentage of aggregate in different particle size ranges to the total volume obtained by the Fuller gradation formula;

Step S12: according to the Monte Carlo principle, randomly generate the parameters of the aggregates in each particle size range, and the parameters include the position and size parameters of the aggregates;

Step S13: Use the obtained aggregate parameters in each particle size range to judge the separation of aggregates, that is, to judge the separation of spherical aggregates, ellipsoid aggregates and random convex polyhedral aggregates, and use Python language to write aggregates Randomly generated phase separation judgment program;

The separation judgment of aggregate mainly includes the validity judgment method of spherical aggregate, the quadratic matrix of space ellipsoid and the validity judgment method of ellipsoid aggregate; among them, the validity judgment method of spherical aggregate is as follows: Spherical aggregate A _i (x _ci , y _ci , z _ci ), spherical aggregate A ₀ (x _c0 , y _c0 , z _c0 ), the radii of spherical aggregate A _i and spherical aggregate A ₀ are r _i , r ₀ , then the judgment equation is

Then, let the coordinates of the lower left corner and upper right corner of the bounding cuboid be (x _L , y _L , z _L ) and (x _U , y _U , z _U ) respectively, the center of each spherical aggregate is A _i , and the spherical The center coordinates are (x _ci , y _ci , z _ci ) and the radius is r _i , then the judgment equation for the separation of spherical aggregate A _i from the boundary is:

The spherical aggregate A ₀ is a random convex polyhedron aggregate generated by the inscribed method on the basis of the spherical aggregate A _i . The positions of the vertices of the random convex polyhedral aggregate A ₀ are random and the spherical surface of the spherical aggregate A _i is circumscribed. , the coordinates of each vertex of the random convex polyhedron are expressed as

In formula (4), the spherical center coordinates of spherical aggregate A ₀ are (x _c0 , y _c0 , z _c0 ), the radius is r ₀ , the coordinates are set to start from the y-axis, and the clockwise direction is positive, α _i is the offset angle from the z-axis, and the clockwise direction is positive, and β _i is the angle rotated around the center of the sphere in the xOy plane;

Then, similarly, let the coordinates of the lower left corner and upper right corner of the bounding cuboid be (x _L , y _L , z _L ) and (x _U , y _U , z _U ) respectively, then the random convex polyhedron aggregate A ₀ and The judgment equation for boundary separation is:

The method for judging the validity of ellipsoid aggregates is: set the quadratic forms of ellipsoid A and ellipsoid B as X ^T AX=0 and X ^T BX=0, respectively, then the generalized characteristic polynomials of ellipsoid A and ellipsoid B are for

f(λ)=det(λA+B),

If the equation f(λ)=0 has two different positive real roots, then ellipsoid A and ellipsoid B are separated; otherwise, ellipsoid A and ellipsoid B intersect;

Then, the method for judging the separation of the ellipsoid aggregate from the boundary is: combine the equations of the ellipsoid and the plane to obtain the matrix equation

是一个三阶对称方阵，In formula (6),

is a third-order symmetric square matrix,

若矩阵A和B满足条件|A|>0且(a₁₁+a₂₂)|B|<0，则椭球与平面相交，否则，椭球与平面相离；let matrix

If the matrices A and B satisfy the conditions |A|>0 and (a ₁₁ +a ₂₂ )|B|<0, then the ellipsoid intersects the plane, otherwise, the ellipsoid is separated from the plane;

Use Python language to write random generation programs for spherical aggregates, ellipsoid aggregates and convex polyhedral aggregates;

Step S14: Embed the Python program of the foregoing judgment result into ABAQUS to generate a three-dimensional random aggregate geometric model.

Step S2: Based on the concrete three-dimensional random aggregate model established in step S1, define the aggregate unit, and at the same time define the mortar unit according to the size of the concrete specimen, and establish a three-dimensional multiphase mesoscopic model of the non-uniform concrete in the interface transition zone;

The specific steps to establish a 3D multiphase mesoscopic model are as follows:

Step S21: To establish a three-dimensional multiphase meso-model, it is necessary to define the tensile-plastic damage constitutive relation and determine the material parameters. The tensile-plastic damage constitutive relation formula is:

In formula (7), σ _tu is the peak stress of the material, G _f is the fracture energy, and u ^ck is the cracking displacement; in the established three-dimensional multiphase mesoscopic model, the constitutive relationship and the damage evolution equation of the softening section are determined by the material. The peak stress, the fracture energy G _f and the cracking displacement u ^ck are controlled by , where σ _tu and G _f are the material constants of the concrete specimen, which can be measured by experiments, so the stress value and the damage variable are both functions of the cracking displacement u ^ck , the stress change of the damaged element is not related to the element size in the actual calculation, which greatly reduces the mesh sensitivity of the model;

Step S22: Establish a three-dimensional multiphase mesoscopic model of the non-uniform concrete in the interface transition zone. The thickness and strength of the interface transition zone change with the change of the aggregate particle size, including that the thickness of the interface transition zone is linearly proportional to the aggregate particle size. The strength of the interface transition zone has an exponential function relationship with the thickness of the interface transition zone. Here, the non-uniformity of the interface transition zone is considered, that is, the thickness and strength of the interface transition zone outside each aggregate change with the change of aggregate particle size. It truly reflects the mechanical properties of the interface transition zone; the relationship between the strength of the interface transition zone and the thickness of the interface transition zone is:

ξ=e ^bδ-c +d (8)

In formula (8), ξ is the ratio of the strength of the interface transition zone to the mortar strength, δ is the thickness of the interface transition zone, c and d are the parameters of the exponential function, the coordinates of two points (δ _min , ξ _max ) and (δ _max , ξ _min ) is substituted into the expression to obtain;

Step S23: Based on formula (8), determine the material parameters of the concrete specimen, substitute the determined mortar strength, interface transition zone strength and fracture energy into formula (7), determine the mortar and interface transition zone plastic damage parameters, use Python script Programmatically generate σ _t -u ^ck and d _t -u ^ck table functions;

Step S24 : wrapping the interface transition area with a thickness outside the aggregate, which is completed by the cutting and merging operations of the Assembly module in ABAQUS.

Step S3: Set up inner and outer mesh transition surfaces for the non-uniform concrete three-dimensional multiphase mesoscopic model of the interface transition area; arrange high-density (smaller mesh) meshes in the key research area (ie, the interface transition area), and the seed size It is equivalent to its thickness, and sparse (larger mesh) meshes are arranged in the aggregate unit and the mortar unit. Since the unit size of the interface transition area is small, it is set at the junction of the interface transition area, the aggregate unit and the mortar unit respectively. The mesh transition surface makes the transition from the high-density mesh of the interface transition area to the sparse mesh of the aggregate element and mortar element to make a smooth transition. The computational efficiency of the meso-model;

The method of establishing the mesh transition surface is to establish a concentric surface concentric with the aggregate centroid and different particle size in the aggregate unit inside the interface transition area and the mortar unit outside the interface transition area. The establishment process also uses Python. Script programming is implemented, embedded in ABAQUS to complete the automatic generation of inner and outer mesh transition surfaces.

Step S4: Based on the model obtained in Step S3, use the displacement loading method to perform numerical simulation of the three-dimensional failure failure process of the concrete specimen;

Step S41 : applying boundary conditions to the non-uniform concrete three-dimensional multiphase mesoscopic model of the interface transition zone to be tested, and applying displacement loads at the loading points;

Step S42: Set the damage threshold. When the tensile damage value reaches the damage threshold, it is determined that the unit fails and breaks down. The larger the damage value is, the more serious the material failure is. The damage threshold is set to 0.9, that is, when the tensile damage value reaches the damage threshold At the threshold value, the failure of the unit is considered to be fracture failure; in uniaxial tension, the damage evolution process and failure failure mode of multiple sections of the concrete specimen are analyzed. The three-dimensional failure and damage process is analyzed, and then the damage cloud image of the transition zone of the interface inside the concrete specimen is compared with the macro damage cloud image of the outer side of the concrete specimen, which more clearly shows the damage evolution process of the concrete specimen as a three-dimensional spatial structure;

Step S43: Store the acquired damage value in the result information matrix, build and solve the model in ABAQUS, and process the elements in the result information matrix after the calculation to complete the simulation of the three-dimensional damage evolution process and fracture shape of the concrete specimen.

In order to verify the accuracy of the model provided in this application, this application has carried out specific examples. In the examples, it is determined based on the Fuller gradation formula that the aggregate particle size range is 5mm-20mm, then the particle size is in the range of 15mm-20mm The percentage of aggregate in the aggregate volume is 13.4%, the percentage of aggregate with particle size in the range of 10mm-15mm is 15.9%, and the percentage of aggregate with particle size in the range of 5mm-10mm is 15.9%. The percentage of the total volume of the feed was 20.7%. In order to ensure the smooth delivery of large-diameter aggregates, the random generation of aggregate parameters is performed according to the order of aggregate particle size range from large to small.

The number of aggregates in each particle size range is determined by formula (2). The size of the cube specimen is 100mm×100mm×100mm, and 24 aggregates with particle size in the range of 15mm-20mm are put in, and the particle size is in the range of 10mm-15mm. 78 aggregates were put in, and 469 aggregates with particle size in the range of 5mm-10mm were put in.

Then, according to the Monte Carlo principle, the random generation of each parameter of the aggregate mainly includes the position parameter of the aggregate (that is, the aggregate center coordinate) and the size parameter (that is, the aggregate particle size). As explained above, the aggregate forms are mainly spherical aggregates, ellipsoid aggregates and convex polyhedron aggregates, mainly including the effectiveness judgment method of spherical aggregates, the quadratic matrix of space ellipsoids and ellipsoid aggregates. The validity judgment method, etc., adopt the Python language to write the separation judgment program of the random generation of aggregates, in the embodiment, use the linalg.eig() function in the SciPy module of the Python language to solve the generalized eigenvalue of the characteristic equation, because linalg When the .eig() function solves the generalized eigenvalues, the generalized characteristic polynomial is defined as f(λ)=det(λA-B). In this embodiment, adding a negative sign before the matrix A makes the generalized eigenvalues judged by the program actually The characteristic equation becomes f(λ)=det(-λA-B)=0, and both sides of the equation are multiplied by -1 to obtain det(λA+B)=0, and the generalized eigenvalue obtained at this time is the desired value.

The three-dimensional multiphase mesoscopic model of the non-uniform concrete in the interface transition zone established in the embodiment, the obtained ratio ξ and the relationship curve of the interface transition zone thickness δ are shown in Figure 2; when determining the material parameters, after trial calculation, in the formula ( 8) Take b=-7.5, the elastic modulus of the interface transition zone is taken as 60%-80% of the mortar matrix, the strength is taken as 35%-65% of the mortar matrix, and the fracture energy is taken as 40%-90% of the mortar matrix , the mechanical parameters of each phase material of concrete are shown in Table 1 below;

Table 1 Material mechanical parameters of concrete phases

According to Table 1, the material parameters such as tensile strength and fracture energy of mortar and interface transition zone are substituted into formula (7) to complete the determination of plastic damage parameters of mortar and interface transition zone (ITZ), and use Python script programming to generate σ _t -u ^ck and d _t -u ^ck table function; wrap the interface transition area with equal thickness outside the aggregate, and use the cutting (Cut) and merging (Merge) operations of the Assembly module in ABAQUS to complete the whole process using Python language programming. A good demonstration of the morphology of the interfacial transition zone is shown in Figure 3a–Figure 3b, which give a schematic diagram of the interfacial transition zone between ellipsoidal aggregates and convex polyhedral aggregates.

In order to effectively reduce the number of elements, it is necessary to set up a mesh transition surface in the interface transition area and the interface area between the internal aggregate and external mortar, so as to realize the small-sized mesh of the interface transition area to the large-sized mesh of aggregate and mortar. To achieve a natural and smooth transition, the purpose of this approach is to further improve the accuracy of the experimental simulation. As shown in Figure 4a-Figure 4b, the meshing schematics of the ellipsoid aggregate and the convex polyhedron aggregate are shown.

The next step is to use the displacement loading method to simulate the three-dimensional failure and failure process of the concrete specimen. The embodiment gives the following simulation process:

First, the corresponding boundary conditions are applied to the three-dimensional multiphase mesoscopic model of concrete under study, displacement load is applied at the loading point, and uniform surface load is applied to the right boundary of the uniaxial tensile specimen;

In the embodiment, the size of the concrete specimen is 100mm×100mm×100mm, and the aggregate particle size is 5mm-20mm. A uniform displacement load of 0.25mm is applied to the right end of the piece;

Second, use the damage cloud map at the end of the ABAQUS calculation to describe the failure failure form and damage fracture degree of the material. DAMAGET represents the tensile damage value of the material. The range of DAMAGET is between 0 and 1. The larger the damage value, the material failure. The more serious the damage is, the damage threshold is set to 0.9. When the tensile damage value reaches the damage threshold, it is considered that the unit fails and breaks down;

Third, analyze the damage evolution process and failure failure mode of the uniaxial tensile concrete specimen along the X-direction 30%, 60% and 90% sections (respectively referred to as I section, II section, and III section). The final damage cloud images of each section of the spherical aggregate model are shown in Figures 5a-5c, which represent Section I, Section II, and Section III, respectively;

Fourth, the model was established and solved in ABAQUS, and the overall fracture diagram (Fig. 6a) and fracture morphology (Fig. 6b) at the end of model loading were obtained. Since the plastic damage model is used for numerical calculation, there are often multiple incremental _{displacement loading steps} in the calculation process. The damage of the structure is extracted under the four loading steps of u _max to analyze the failure and failure process inside the structure, and the damage and fracture conditions of each section inside the specimen are compared with the macroscopic damage and fracture conditions outside the specimen, obtained from Figure 6b In the damage cloud diagram of , the unit of the cluster represents the fracture failure of the material, and the damage value of the unit inside the model varies between 0 and 1.

It can be seen that the three-dimensional multiphase mesoscopic model established by the present application fully considers the characteristics of the interface transition zone, and can clearly demonstrate the damage evolution process of concrete as a three-dimensional spatial structure.

It will be understood by one of ordinary skill in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as herein, are not to be taken in an idealized or overly formal sense. explain.

The meaning of "and/or" described in this application means that each of them exists alone or both are included.

The meaning of "connection" described in this application may be a direct connection between components or an indirect connection between components through other components.

Taking the above ideal embodiments according to the present invention as inspiration, and through the above description, relevant personnel can make various changes and modifications without departing from the technical idea of the present invention. The technical scope of the present invention is not limited to the contents in the specification, and the technical scope must be determined according to the scope of the claims.

Claims (8)

1. the establishment of a concrete three-dimensional multiphase mesoscopic model and the numerical simulation method, it is characterized in that: specifically comprise the following steps: Step S1: establishing a concrete three-dimensional random aggregate model, and the concrete three-dimensional random aggregate model includes a three-dimensional spherical aggregate model, a three-dimensional ellipsoid aggregate model, and a three-dimensional random convex polyhedron aggregate model; Step S2: Based on the concrete three-dimensional random aggregate model established in step S1, define the aggregate unit, and at the same time define the mortar unit according to the size of the concrete specimen, and establish a three-dimensional multiphase mesoscopic model of the non-uniform concrete in the interface transition zone; Step S3: setting the inner and outer mesh transition surfaces for the non-uniform concrete three-dimensional multiphase mesoscopic model of the interface transition zone; Step S4: Based on the model obtained in Step S3, use the displacement loading method to perform numerical simulation of the three-dimensional failure and failure process of the concrete specimen. 2. the establishment and numerical simulation method of concrete three-dimensional multiphase mesoscopic model according to claim 1, is characterized in that: in step S1, the step of establishing concrete three-dimensional random aggregate model is specifically: Step S11: Determine the number of aggregates in each particle size range, and use the Fuller gradation formula to obtain the percentage of aggregate in each particle size range to the total aggregate volume. The Fuller gradation formula is:

In formula (1), D ₀ is the diameter of the sieve hole, D _max is the maximum particle size of the aggregate passing through the sieve hole, P _c (D<D ₀ ) is the cumulative volume percentage of aggregate passing through the sieve hole with a diameter of D ₀ , That is, the percentage of aggregate in the particle size range to the total volume; Substitute the percentage of aggregates in the obtained particle size range into the total volume into formula (2) to determine the number of aggregates in each particle size range, formula (2) is:

In formula (2), D _i is the representative particle size of the aggregate in this particle size range, V is the total aggregate volume, and P _ci is the percentage of aggregate volume in this particle size range to the total aggregate volume; Step S12: according to the Monte Carlo principle, randomly generate the parameters of the aggregates in each particle size range, and the parameters include the position and size parameters of the aggregates; Step S13: using the obtained aggregate parameters within each particle size range to judge the separation of aggregates, that is, to judge the separation of spherical aggregates, ellipsoid aggregates and random convex polyhedron aggregates; Step S14: Embed the Python program of the foregoing judgment result into ABAQUS to generate a three-dimensional random aggregate geometric model. 3. The establishment and numerical simulation method of concrete three-dimensional multiphase mesoscopic model according to claim 2, is characterized in that: in step S13, the separation judgment of aggregate mainly comprises the validity judgment method of spherical aggregate, space The quadratic matrix of the ellipsoid and the validity judgment method of the ellipsoid aggregate; Among them, the method for determining the effectiveness of spherical aggregates is: set spherical aggregates A _i (x _ci , y _ci , z _ci ), spherical aggregates A ₀ (x _c0 , y _c0 , z _c0 ), spherical aggregates A _i , the radii of spherical aggregate A ₀ are _ri and r ₀ respectively, then the judgment equation is

Then, let the coordinates of the lower left corner and upper right corner of the bounding cuboid be (x _L , y _L , z _L ) and (x _U , y _U , z _U ) respectively, the center of each spherical aggregate is A _i , and the spherical The center coordinates are (x _ci , y _ci , z _ci ) and the radius is r _i , then the judgment equation for the separation of spherical aggregate A _i from the boundary is:

The spherical aggregate A ₀ is a random convex polyhedron aggregate generated by the inscribed method on the basis of the spherical aggregate A _i . The positions of the vertices of the random convex polyhedral aggregate A ₀ are random and the spherical surface of the spherical aggregate A _i is circumscribed. , the coordinates of each vertex of the random convex polyhedron are expressed as

In formula (4), the spherical center coordinates of spherical aggregate A ₀ are (x _c0 , y _c0 , z _c0 ), the radius is r ₀ , the coordinates are set to start from the y-axis, and the clockwise direction is positive, α _i is the offset angle from the z-axis, and the clockwise direction is positive, and β _i is the angle rotated around the center of the sphere in the xOy plane; Then, similarly, let the coordinates of the lower left corner and upper right corner of the bounding cuboid be (x _L , y _L , z _L ) and (x _U , y _U , z _U ) respectively, then the random convex polyhedron aggregate A ₀ and The judgment equation for boundary separation is:

The method for judging the validity of ellipsoid aggregates is: set the quadratic forms of ellipsoid A and ellipsoid B as X ^T AX=0 and X ^T BX=0, respectively, then the generalized characteristic polynomials of ellipsoid A and ellipsoid B are for f(λ)=det(λA+B), If the equation f(λ)=0 has two different positive real roots, then ellipsoid A and ellipsoid B are separated; otherwise, ellipsoid A and ellipsoid B intersect; Then, the method for judging the separation of the ellipsoid aggregate from the boundary is: combine the equations of the ellipsoid and the plane to obtain the matrix equation

In formula (6),

is a third-order symmetric square matrix, let matrix

If the matrices A and B satisfy the conditions |A|>0 and (a ₁₁ +a ₂₂ )|B|<0, then the ellipsoid intersects the plane, otherwise, the ellipsoid is separated from the plane. 4. the establishment and numerical simulation method of concrete three-dimensional multiphase mesoscopic model according to claim 3, it is characterized in that: in step S2, the concrete steps of setting up interface transition zone non-uniform concrete three-dimensional multiphase mesoscopic model are: Step S21: Define the tensile-plastic damage constitutive relation and determine the material parameters. The tensile-plastic damage constitutive relation formula is:

In formula (7), σ _tu is the peak stress of the material, G _f is the fracture energy, and u ^ck is the cracking displacement; Step S22 : establishing a three-dimensional multiphase mesoscopic model of the non-uniform concrete in the interface transition zone, including a linear proportional relationship between the thickness of the interface transition zone and the aggregate particle size, and an exponential function relationship between the strength of the interface transition zone and the thickness of the interface transition zone. The relationship between the strength of the transition zone and the thickness of the interface transition zone is ξ=e ^bδ-c +d (8) In formula (8), ξ is the ratio of the strength of the interface transition zone to the mortar strength, δ is the thickness of the interface transition zone, c and d are the parameters of the exponential function, the coordinates of two points (δ _min , ξ _max ) and (δ _max , ξ _min ) is substituted into the expression to obtain; Step S23: Based on formula (8), determine the material parameters of the concrete specimen, substitute the determined mortar strength, interface transition zone strength and fracture energy into formula (7), determine the mortar and interface transition zone plastic damage parameters, use Python script Programmatically generate σ _t -u ^ck and d _t -u ^ck table functions; Step S24 : wrapping the interface transition area with a thickness outside the aggregate, which is completed by the cutting and merging operations of the Assembly module in ABAQUS. 5. The establishment and numerical simulation method of concrete three-dimensional multiphase mesoscopic model according to claim 4, it is characterized in that: in step S3, arrange high-density mesh in the interface transition zone, the seed size is equivalent to its thickness, in the bone The material unit and the mortar unit are arranged with sparse meshes, and at the same time, a mesh transition surface is set at the junction of the interface transition area with the aggregate unit and the mortar unit respectively, so that the high-density meshes in the interface transition area are connected to the aggregate unit and the mortar unit. Sparse mesh for smooth transitions. 6. The establishment and numerical simulation method of concrete three-dimensional multiphase mesoscopic model according to claim 5, is characterized in that: the establishment method of grid transition surface is, in the aggregate unit inside the interface transition zone, the interface transition zone In the outer mortar unit, a concentric surface concentric with the aggregate centroid and different particle size is established respectively. 7. The establishment and numerical simulation method of concrete three-dimensional multiphase mesoscopic model according to claim 5, is characterized in that: the concrete steps of step S4 are: Step S41 : applying boundary conditions to the non-uniform concrete three-dimensional multiphase mesoscopic model of the interface transition zone to be tested, and applying displacement loads at the loading points; Step S42 : setting a damage threshold, when the tensile damage value reaches the damage threshold, it is determined that the unit fails to cause fracture damage. The larger the damage value is, the more serious the material failure and damage is, and the damage threshold is 0.9; Step S43: Store the acquired damage value in the result information matrix, and process the elements in the result information matrix after the calculation to complete the simulation of the three-dimensional damage evolution process and fracture shape of the concrete specimen. 8. the establishment and numerical simulation method of concrete three-dimensional multiphase mesoscopic model according to claim 7, it is characterized in that: when carrying out test simulation to concrete three-dimensional multiphase mesoscopic model, after setting damage threshold, calculate with ABAQUS The damage cloud map at the end describes the failure failure mode and damage fracture degree of the material; At the same time, when the load is applied to the lateral boundary of the uniaxial tensile specimen, the damage evolution process and failure failure mode of multiple sections of the concrete specimen are analyzed.

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